As mentioned previously, however, the constraints (I) and (II) do not quite fix the unitary time evolution characteristic of quantum dynamics. For this, some additional inputs are required; whether that be in the form of a quantum potential, as we have employed here, or through additional constraints besides that (see e.g., [1]}). In any case, the ability in ED to separate models into quantum/non-quantum should be considered a feature of the approach, as this allows an assessment of the conditions under which that linear structure may emerge, and those situations in which it does not. To this end, among the central results of this thesis is that quantum field theory in a curved space-time emerges rather naturally on the basis of the constraints (I) and (II), plus a quantum potential, so long as the background is fixed. The situation of a dynamical background, on the other hand, is qualitatively different. The ingredients that lead to a full quantum theory in the context of a fixed background, no longer do so when the background is allowed to evolve. It is, in fact, a fundamental aspect of the coupling of quantum scalar fields to a dynamical background that the theory will instead be nonlinear. While surely one expects a regime in which these nonlinearities can be neglected and we recover the standard quantum field theory in curved space-time, this must be regarded only as an approximation to the full dynamics. In this approach there is thus no unitary time evolution, nor any quantum superposition principle. Period.
